The Handbook of Portfolio Mathematics: Formulas for Optimal Allocation & Leverage (Wiley Trading) (Hardcover)

by Ralph Vince (Author)

Editorial Reviews

Product Description
The Handbook of Portfolio Mathematics

"For the serious investor, trader, or money manager, this book takes a rewarding look into modern portfolio theory. Vince introduces a leverage-space portfolio model, tweaks it for the drawdown probability, and delivers a superior model. He even provides equations to maximize returns for a chosen level of risk. So if you're serious about making money in today's markets, buy this book. Read it. Profit from it."
—Thomas N. Bulkowski, author, Encyclopedia of Chart Patterns

"This is an important book. Though traders routinely speak of their 'edge' in the marketplace and ways of handling 'risk,' few can define and measure these accurately. In this book, Ralph Vince takes readers step by step through an understanding of the mathematical foundations of trading, significantly extending his earlier work and breaking important new ground. His lucid writing style and liberal use of practical examples make this book must reading."
—Brett N. Steenbarger, PhD, author, The Psychology of Trading and Enhancing Trader Performance

"Ralph Vince is one of the world's foremost authorities on quantitative portfolio analysis. In this masterly contribution, Ralph builds on his early pioneering findings to address the real-world concerns of money managers in the trenches-how to systematically maximize gains in relation to risk."
—Nelson Freeburg, Editor, Formula Research

"Gambling and investing may make strange bedfellows in the eyes of many, but not Ralph Vince, who once again demonstrates that an open mind is the investor's most valuable asset. What does bet sizing have to do with investing? The answer to that question and many more lie inside this iconoclastic work. Want to make the most of your investing skills Open this book."
—John Bollinger, CFA, CMT, www.BollingerBands.com

From the Inside Flap

Ralph Vince has made many contributions to the world of money management in trading over the course of his career, and his thoughts on this subject have captured the attention of both financial professionals and savvy individual traders alike. In The Handbook of Portfolio Mathematics, Vince outlines the essential elements found in his first three groundbreaking books—Portfolio Management Formulas, The Mathematics of Money Management, and The New Money Management—and then presents you with new insights that will allow you to implement his ideas in real-world trading situations. For instance, this book discusses drawdown beyond any discussion of drawdown to date. Vince's new portfolio model, the Leverage Space Model, uses drawdown as its risk metric, as opposed to conventional methods which use variance in returns. The result is a portfolio model far superior to any of its predecessors—some of which have been in use throughout the industry for over half a century.

While the first part of this book is purely conceptual, it is also exhaustive in that sense; not on portfolio construction in general, but rather, on portfolio construction in terms of optimal position sizes along the lines of an Optimal f approach. But The Handbook of Portfolio Mathematics goes far beyond theoretical principles; it quickly takes you from basic gambling theory and statistics, through the introduction of the Kelly criterion, Optimal f, and finally onto the leverage space portfolio model for multiple-simultaneous positions. The Handbook of Portfolio Mathematics also tackles the mathematical puzzle posed by attempting to employ such complex concepts and includes discussions of:

• How the Optimal f framework can be applied with regard to risk of financial ruin and its more familiar, and real-world-applicable cousin, risk of drawdown

• Reinvestment of returns and geometric growth issues

• Laws of growth, utility, and finite streams

• Classical portfolio construction

• The geometry of mean variance portfolios

• The common denominators—in terms of portfolio and systems management—that seem to be shared among the more successful commodities funds

The Handbook of Portfolio Mathematics is not entirely about trading the markets. It's about very basic, mathematical laws and how they affect us when we engage in a stream of risk-related outcomes that we don't have any control over. Written in an engaging and informative style, this book will guide you through a maze of complex theoretical issues, while arming you with a set of distinct formulas that can be used to achieve optimal fund allocation and leverage, as well as maximum portfolio returns.

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Product Details

• Hardcover: 448 pages
• Publisher: Wiley; illustrated edition edition (May 25, 2007)
• Language: English
• ISBN-10: 0471757683
• ISBN-13: 978-0471757689
• Product Dimensions: 9.1 x 6.1 x 1.5 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars See all reviews (7 customer reviews)
• Amazon.com Sales Rank: #411,967 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

20 of 21 people found the following review helpful:

5.0 out of 5 stars Optimal learning, November 7, 2007

By	John Bollinger - See all my reviews (REAL NAME)

This is quite simply the most important investment book that you haven't read yet. Mr. Vince explains in a clear and forthright manner why position sizing is so important, demonstrates the importance of getting it right and shows you how to determine the correct position size for your approach.

While Mr. Vince's past books were good, "The Handbook of Portfolio Mathematics" is a quantum leap forward. It brings together all his prior research and couples it with the benefit of many years worth of real-time application of his principals. The exposition is rigorous for those who want to delve into the math, while the prose allows the less mathematically inclined reader full access to his ideas.

Mr. Vince stands on the shoulders of giants here. Claude Shannon and John L. Kelly laid out the basic framework as part of their research into communication theory and all too slowly it has been taken up by the investment community. The seminal paper in this area is Kelly's 1956 "A New Interpretation of Information Rate".

Don't believe Mr. Vaibhav for even a second when he says that the material is this book is "not useful for real life applications". Nothing could be farther from the truth. The material in this book is not only applicable, it is essential in real-world applications. How else are you going to know how much to invest in any given transaction? Invest too much and run the risk of ruin, invest too little and you defeat your 'edge'. (The Ryan formula he references leads directly to underperformance.)

Again, ignore Mr. Vaibhav when he suggests that there is too much volatility in this approach, which suggests that either he hasn't read this work or hasn't comprehended it. The volatility is a function of your edge and can be tamed to suit your preference in any number of ways. For example, in a pure optimal f application the trade-off between growth rate and volatility is absolutely clear cut and position size can be tailored to one's risk and reward preferences. You may not like the volatility that goes with straight optimal f, but if your want to grow your portfolio at its full potential rate, you'll accept it.

I have known Mr. Vince for many years and he is quite simply one of the brightest minds in the industry. Do not miss this opportunity to share his insights into the investment process.

John Bollinger, CFA, CMT
President Bollinger Capital Management

2 of 2 people found the following review helpful:

5.0 out of 5 stars If You Want To Be More Profitable -- Buy This Book Today, October 28, 2008

By	Amazon Book Lover (USA) - See all my reviews

This book is Vince's best book, and incorporates all the new knowledge he has accumulated since the publication of his earlier work. The more we are able to refine our money management and risk control the more profitable we will ultimately be. And, this book clearly shows you how to refine your skills in this area - and how to be confident enought to risk the right amount to maximize your return.

Your confidence after reading this book will be gained from learning how to calcualte "relevant" risk amounts for each trade based on your current win ratio and payoff ratio by using the optimal f formulas. Vince is a skilled mathematician, and even if you are not, you can use his approach to obtain "relevent" data. Meaning -- don't just guess at what amount to risk, instead determine what your performance statistics are and base your decisions on that -- not on what another trader or educator suggests.

In addition to this book by Vince, two other must have books on this subject are Balsara's "Money Management Strategies For Futures Traders" and McDowell's "A Trader's Money Management System".

A Trader's Money Management System: How to Ensure Profit and Avoid the Risk of Ruin (Wiley Trading)

Money Management Strategies for Futures Traders (Wiley Finance)

With these three books you will have the foundation to confidently increase your profits by risking the right amount on every trade for optimal returns.

19 of 27 people found the following review helpful:

2.0 out of 5 stars High level Mathematics but not useful for real life applications., September 10, 2007

By	Joshi Vaibhav - See all my reviews (REAL NAME)

Ok. To begin with I am giving only 2 stars for this book , and the reason for this high rating is some good mathematics it covers.

Part 1 of the book covers statistics, normal distribution, binomial distribution and all other concepts applied to trading systems. However this has been covered inadequately. Author should have either presumed that people reading this book are already aware of this and avodied it altogether or he should have covered it in enough details. Some 150 pages are lost on this but again 150 pages are not enough for covering all this material. The examples given are kind of weird, one page author speaks of coin toss examples and immediately after that he goes to example of horse racing and its probabilities. Instead it would have been great had he taken single example of a trading system and evolved his work around it.

Part 2 of the book comes back to Vince favourite concept of optimal F. Another 100 pages are spent on this. The problem is nobody in real life is going to trade optimal F as it is too risky to trade in real life. The whole discussion rounds on optimal f, its characteristics etc.

These two sections (part 1 & 2 ) are straight from Ralph Vince previous books. So in case you have read those books then there is nothing new here.

Part 3 is where it becomes slightly interesting. Author speaks about portfolio management, space leveraged model, and gives overview of what professionals have done. But all the computations on this are presuming that you are trading optimal F. In case you have already decided not to trade optimal f as it is too risky, then there is not much advise here for you on how to adjust your portfolio. The section on "What professionals have done" is slightly interesting though.

The whole book is full of complex mathematics (You must have done majors in mathematics at graduation level in your college), and author presumes that you know most of that mathematics so there is little explaination for those notations.

The book may be interesting for a large futures fund who can afford to employ an army of mathematicians and programmers to try all those concepts. However if you trade for yourself, or have a small fund then you are not likely to gain much from the book. If you have read any of Ralph Vince previous books then I will suggest not to go for this one.

I will rate Ryan Jones "The number Game" much higher on subject of money management for its ease of application in real life.